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[1800GAMBLER]

You now have three jugs, capable of holding 8 litres, 5 litres and 2 litres respectively.
Initially the 8 litre jug is full, and the others are empty. You are allowed to pour
the contents of any jug into another until either the first jug is empty or the second
is full. After a certain time, there are a litres in the 8 litre jug, b in the 5 litre jug
and c in the 2 litre jug. What are the possible values of (a, b, c)? Can you explain
why these are the only possibilities?

[tpir90036]

<font color="white">using the jugs (he he he) to add and subtact off of one another it is possible that A can be anything from 1-8, B can be anything from 0-5 and C can be anything from 0-2. but obviously A+B+C = 8 has to hold. and for C to be 1, B must be either 5,4 or 0 since we have to use it to subtract off the 1.

[1, 5, 2], [2, 5, 1], [2, 4, 2], [3, 5, 0], [3, 4, 1], [3, 3, 2], [4, 4, 0], [4, 2, 2], [5, 3, 0], [5, 1, 2], [6, 2, 0]
[6, 0, 2], [7, 1, 0], [7, 0, 1], [8, 0, 0]

i think that might be too many. but someone else can correct it since i am hungry and need to go get some food.

-tpir
</font>

[ctide]

<font color="white">
a = 8, b = 0, c = 0
a = 6, b = 0, c = 2
a = 6, b = 2, c = 0
a = 4, b = 2, c = 2
a = 4, b = 4, c = 0
a = 3, b = 5, c = 0
a = 2, b = 5, c = 1
a = 2, b = 4, c = 2
a = 1, b = 5, c = 2
</font>

Missed one.